Not everyone is such a fan … Barack Obama is lifted off the ground by Scott Van Duzer. Photograph: Pablo Martinez Monsivais/AP

Barack Obama's campaign team has published an extensive critique of a documentary which accuses the US president of being an anti-colonialist who will work to reduce his country's influence on world affairs if he is re-elected this winter.

2016: Obama's America, directed by Indian-American conservative author and commentator Dinesh D'Souza, has been a surprise box office success in the US this summer. As of last weekend, it had taken $26.2m (£16.3m), behind only Michael Moore's anti-George W Bush polemic Fahrenheit 9/11 in the pantheon of US political documentaries.

D'Souza's film argues the president's political instincts are anti-American – allegedly due to the influence of his supposedly anti-colonialist Kenyan father, Barack Obama Sr. It warns that a second term for the Democratic candidate after November's presidential election could change the country for good, and ends with the statement: "The future is in your hands."

Obama's re-election team hit back on Wednesday with an online post via the campaign website BarackObama.com. "That his writings and film are based on lies should not come as a surprise to anyone given D'Souza's long history of attempting to add a veneer of intellectual respectability to fringe theories, conspiratorial fear-mongering, and flat-out falsehoods," it reads.

"Right-wing author Dinesh D'Souza has recently released 2016: Obama's America, a movie that falsely smears President Obama as having a hidden agenda bent on realising 'anti-colonial' ambitions'," the post begins, before quoting a series of poor verdicts on the film and its director's previous work across a range of media.

"A self-proclaimed expert on the president, D'Souza bases the film around his own past works, which were previously described as 'the worst kind of smear journalism,' and riddled with 'lazy' errors," the post continues. "The result is what Variety calls a 'cavalcade of conspiracy theories, psycho-politico conjectures and incendiary labelling' and what the LA Times labels a 'badly disguised and overly long attack ad'. A look at D'Souza's record is a look at a history of demonstrably false and ridiculous claims about the president, and 2016 is no exception. In fact, admitting President Obama was born in the US is what Bloomberg calls 'as close to moderation as this nutty film gets'."

It adds: "2016 promises to show viewers what they 'don't know' about President Obama, but instead reveals what Newsday called a 'ranter' peddling conspiracy theories. In place of an actual documentary, D'Souza employs 'pseudo-scholarly leaps of logic' to invent an imaginary character who has inherited 'anti-colonial,' 'Third World' views from his father — whom he last saw when he was 10 years old."

Obama's team also suggests that D'Souza once falsely accused the president of backing the release of the Lockerbie bomber, despite his administration having stated its opposition to the move and written to the Scottish government to raise its strong objection. The team alleges that D'Souza once accused Obama of authorising the US bank bailouts when it was George W Bush who signed the troubled asset relief programme into law in October 2008.

D'Souza, meanwhile, hit back in an interview with the Hollywood Reporter. "Their original strategy was to lie low and hope this goes away, but now they're launching a full-scale attack," he said. "And this is one of the most bizarre, clumsy and ineffective attacks I have seen in politics. Half of the stuff they talk about isn't even in the film – like the Lockerbie bomber. These guys are referencing a Columbia Journalism Review article that's two years old and is about my book, not about the film."

D'Souza pointed out that Obama's team made no mention of the interview the commentator conducted with the president's Kenyan half-brother, George Obama, who lives in Huruma Flats near Nairobi, and who the film-maker claims lives in poverty.

"If Mitt Romney had a half brother living destitute in a third-world slum, it would be on the front page of the New York Times and a topic on MSNBC, CBS News and the Sunday talk shows," said D'Souza. "But this fact is not even reported by those outlets. They just pretend it doesn't exist. It's immensely interesting that a guy who has more than 50 times quoted the Bible – 'we are our brother's keeper' – has a half-brother he won't help at all. That's not a story?"